Film Flow in Liquid Helium II at Low Level Differences

Observations of the flow of the liquid helium II film have been made at very low level differences. To produce the flow a plunger is displaced vertically at an accurately controlled rate inside of a beaker of internal diameter of about one centimeter. By this means the initial behavior when flow is started, the eventual steady-state behavior, and the oscillations around the final equilibrium position after the plunger is stopped, are observed. The results obtained fit the form of equations derived by Atkins if, in addition, the existence of an upper limit to the velocity of flow is postulated. However, the period of the final oscillations is always found to be shorter than that deduced from the initial effects. The final periods also vary more slowly with temperature and more rapidly with the total length of the helium film than do the initial periods. Assuming the film thickness $d$ varies with height $h$ according to a relation $d=\frac{D}{h^n}$, we find from the initial periods that $n\cong \frac{1}{2}$ and from the final oscillations $n\cong 1$. $D$, the thickness at a height of one centimeter, is approximately 2.5×${10}^{-6\mathrm{}}$ cm, somewhat smaller values being obtained from the initial periods than from the final periods.